Mathematical Notation


Set Membership: x in S
True iff x is an element of the set S.

Set Comprehension: { x | p }
The set of elements x satisfying predicate p.

Relations and Partial Functions

Relation: A relation is a set of pairs, e.g., R = { (x,y) | p } , and x is related to y by R if (x,y) in R.

Domain: (dom R) = { x | ?y. (x,y) in R }

Range: (ran R) = { y | ?x. (x,y) in R }

Partial Function: A partial function is a relation in which each domain element x has at most one corresponding range element y.

Application: If f is a partial function, and x in dom f, then we write f(x) for that unique y corresponding to x in f.


Array Declaration: s : ARRAY OF T
Declares s to be an array of elements of type T.

Array Size: #s

Array Indexing: s[i]
The first element of s is s[0], while the last element is s[#s-1].


Less than or equal to: E <= F

Greater than or equal to: E >= F